Minimum MS. E. Gerber's Lemma

Or Ordentlich*, Ofer Shayevitz

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Mrs. Gerber's Lemma lower bounds the entropy at the output of a binary symmetric channel in terms of the entropy of the input process. In this paper, we lower bound the output entropy via a different measure of input uncertainty, pertaining to the minimum mean squared error prediction cost of the input process. We show that in many cases our bound is tighter than the one obtained from Mrs. Gerber's Lemma. As an application, we evaluate the bound for binary hidden Markov processes, and obtain new estimates for the entropy rate.

Original languageAmerican English
Article number7271092
Pages (from-to)5883-5891
Number of pages9
JournalIEEE Transactions on Information Theory
Issue number11
StatePublished - 1 Nov 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.


  • Binary symmetric channel
  • Mrs. Gerber's lemma
  • hidden Markov process


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